Rapid stress birefringence mapping in mounted curved lenses with a curved-layer Jones approximation

Abstract

We develop a curved-layer Jones approximation for rapid stress birefringence mapping in mounted curved lenses. Fixed pupil columns on swept finite element layers replace repeated three-dimensional stress queries while retaining the stress-optic relation and ordered Jones propagation. Against a fine refracted reference on the same mesh, the representative lens gives a retardance root mean square (RMS) residual of 0.0798 mrad and a Pearson correlation of 0.9993. At equal Jones depth, the curved-layer calculation takes 0.0112 s, compared with 0.132 s for refracted sampling, which reduces the residual to 2.55 × 10 −4 mrad. Across five curvatures, the three cases with maximum lateral ray displacement no greater than 3.72% of the clear aperture radius remain below 5% relative RMS residual and 0.5 mrad maximum local residual under the stated mounting conditions. At greater curvature, both the sampled stress history and path length contribute to the error, and the residual reaches 2.84 mrad. The method links geometric displacement to numerical accuracy and computation time for field screening of mounted lenses.